A simple model of growth cycles with technology choice

Yosuke Umezuki, Masanori Yokoo

Research output: Contribution to journalArticle

Abstract

In this study, we develop a simple, computable overlapping generations model that exhibits endogenous fluctuations. The key assumption is that a firm can choose from multiple technologies of production. Since the model reduces to a piecewise linear map on the unit interval, it allows us to conduct an in-depth analysis of its dynamic properties. Particularly, this piecewise linearization reveals the ability of the model to exhibit periodic attracting cycles of an arbitrarily large period as well as non-periodic attractors. Furthermore, it is demonstrated that the occurrence of periodic patterns is completely characterized by the rotation number or the “devil's staircase.”

Original languageEnglish
Pages (from-to)164-175
Number of pages12
JournalJournal of Economic Dynamics and Control
Volume100
DOIs
Publication statusPublished - Mar 1 2019

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Cycle
Devil's Staircase
Piecewise Linear Map
Overlapping Generations
Rotation number
Dynamic Properties
Linearization
Attractor
Choose
Model
Fluctuations
Interval
Unit
Growth cycle
Technology choice
Overlapping generations model
Endogenous fluctuations
Business

Keywords

  • Devil's staircase
  • Endogenous fluctuations
  • Overlapping generations model
  • Piecewise linearity
  • Rotation number
  • Technology choice

ASJC Scopus subject areas

  • Economics and Econometrics
  • Control and Optimization
  • Applied Mathematics

Cite this

A simple model of growth cycles with technology choice. / Umezuki, Yosuke; Yokoo, Masanori.

In: Journal of Economic Dynamics and Control, Vol. 100, 01.03.2019, p. 164-175.

Research output: Contribution to journalArticle

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